In the general solution (REF ) the constants \({\bf c}_{1,2}\)  determined by initial conditions are explicitly shown.
Vectors \({\bf c}_{1}\)  and \({\bf c}_{2}\)  set independent solutions.
For instance, if \({\bf c}_{1}=0\) , then the radial dependence is
determined by the function \(f^{(2)}(r)\) , and vice versa. If \({\bf c}_{2}=0\)  and \(f^{(1)}(r)=h^{(1)}(n k r)\) , then the field
(REF ) is the multipole expansion [1]}. The
amplitude of electric multipole field is equal to \(a_E (l,m)={c̠}_1 {\bf e}_\theta \) , the amplitude of magnetic multipole field is equal to
\(a_M (l,m)={\bf c}_1 {\bf e}_\varphi \) . So, vector \({\bf c}_1\)  can be called
vector amplitude of multipole fields.
